Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×#19153722 |
| derived, Sylow | C181 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | D181 |
| commutator, hypocenter | C181 | C2×C32 |
| Frattini | C16 | C2×D181 |
| Fitting | C2×C16×C181 | C2 |
| socle, prime radical | C22×C181 | C16 |
| cosocle | C16×C181 | C22 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C2×C16 | |
34 conjugacy classes of subgroups.
2944 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×Dic181, C4×#19153722, #37531854, … |
| maximal normal subgroup of | C32×Dic181, C4×#19153722, #37531854, … |
| maximal quotient of | C4×#19153722, C22⋊#19153722, C4⋊#19153722, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 381);